Abstract: Magnetic reconnection is the main release mechanism of magnetic energy accumulated in the Universe. It is particularly efficient in "low-beta astrophysical plasmas. It converts magnetic energy into heat as well as into the acceleration of bulk plasma flows and energetic particles. In the typically hot and diluted, i.e. collisionless, astrophysical plasmas these processes are essentially kinetic, often turbulent. They have to be described by self-consistently solving Vlasov equations for all species together with Maxwell’s equations for the electromagnetic fields. These challenging problems can currently be solved better and better by using super-computers. This talk will introduce the challenges and review the progress recently made by computer simulations describing the consequences of collisionless magnetic reconnection in strong (guide-) magnetic fields for particle acceleration, of their calibration on observations of the Sun, the solar wind in its interaction with planetary magnetospheres and by laboratory experiments.